A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
Simple Groups - Abstract Algebra
Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order
From playlist Abstract Algebra
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Cyclic Groups (Abstract Algebra)
Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s
From playlist Abstract Algebra
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Bob Oliver: Local structure of finite groups and of their p completed classifying spaces
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
A Tameness Criterion for Generic Modular Mod p Galois Representations by Daniel Le
PROGRAM STATISTICAL BIOLOGICAL PHYSICS: FROM SINGLE MOLECULE TO CELL (ONLINE) ORGANIZERS Debashish Chowdhury (IIT Kanpur), Ambarish Kunwar (IIT Bombay) and Prabal K Maiti (IISc, Bengaluru) DATE & TIME 07 December 2020 to 18 December 2020 VENUE Online 'Fluctuation-and-noise' are themes tha
From playlist Recent Developments Around P-adic Modular Forms (Online)
Pushing back the barrier of imperfection - F-V. Kuhlmann - Workshop 2 - CEB T1 2018
Franz-Viktor Kuhlmann (Szczecin) / 06.03.2018 The word “imperfection” in our title not only refers to fields that are not perfect, but also to the defect of valued field extensions. The latter is not necessarily directly connected with imperfect fields but may always appear when at least
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
John Pardon, Smoothing finite group actions on three-manifolds
2018 Clay Research Conference, CMI at 20
From playlist CMI at 20
CTNT 2020 - Stacky curves in characteristic p - Andrew Kobin
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Smoothing finite group actions on three-manifolds – John Pardon – ICM2018
Topology Invited Lecture 6.13 Smoothing finite group actions on three-manifolds John Pardon Abstract: There exist continuous finite group actions on three-manifolds which are not smoothable, in the sense that they are not smooth with respect to any smooth structure. For example, Bing co
From playlist Topology
Why You'll Never Have A Pet Lion
Episode 4 of 5 Check us out on iTunes! http://testtube.com/podcast Please Subscribe! http://testu.be/1FjtHn5 While they may seem like the same thing at times, there is a vast difference between a tame animal and a domesticated animal. + + + + + + + + Previous Episode: We
From playlist How Domestication Permanently Changed Man And Nature
Monodromy Theorem, Weight Filtration, Weight-Monodromy Theorem
We state Scholze's Theorem and some of the theorems around them. This will be applied later.
From playlist Hodge Theory
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
Fiona Murnaghan: Tame relatively supercuspidal representations
Abstract: Let G be a connected reductive p-adic group that splits over a tamely ramified extension. Let H be the fixed points of an involution of G. An irreducible smooth H-distinguished representation of G is H-relatively supercuspidal if its relative matrix coefficients are compactly sup
From playlist Jean-Morlet Chair - Research Talks - Prasad/Heiermann